Recurrence Plots Of Time Series Research Articles

The Visual Boundary Recurrence Plot: A Closer Look into the Dynamics of Recurrence Plots

In this paper, we introduce a new graphical tool, the visual boundary recurrence plot, in order to provide a more detailed visualization of the well-established method of recurrence plots. In this approach, we are coloring each point of the recurrence plot depending on whether the neighboring points in the vertical and horizontal directions are recurrent or not. We use this plot to study the stability of the textures of the recurrence plots viewing them as geometrical shapes under horizontal and vertical changes. In order to compare two recurrence plots, we define the visual boundary recurrence plot rate distance between their visual boundary recurrence plots to study their closeness/similarity. Finally, we introduce a topological criterion to select an optimal threshold for constructing a recurrence plot. A threshold is optimal when the recurrence plot associated with it remains similar to the ones that are constructed for consecutive values of backwards and forwards thresholds. The results are applied to recurrence plots of time series emanating from different sources: molecular dynamics simulations, Lorenz dynamical system, random noise and daily water level measurements of a river.

Recurrence eigenvalues of movements from brain signals

The ability to characterize muscle activities or skilled movements controlled by signals from neurons in the motor cortex of the brain has many useful implications, ranging from biomedical perspectives to brain–computer interfaces. This paper presents the method of recurrence eigenvalues for differentiating moving patterns in non-mammalian and human models. The non-mammalian models of Caenorhabditis elegans have been studied for gaining insights into behavioral genetics and discovery of human disease genes. Systematic probing of the movement of these worms is known to be useful for these purposes. Study of dynamics of normal and mutant worms is important in behavioral genetic and neuroscience. However, methods for quantifying complexity of worm movement using time series are still not well explored. Neurodegenerative diseases adversely affect gait and mobility. There is a need to accurately quantify gait dynamics of these diseases and differentiate them from the healthy control to better understand their pathophysiology that may lead to more effective therapeutic interventions. This paper attempts to explore the potential application of the method for determining the largest eigenvalues of convolutional fuzzy recurrence plots of time series for measuring the complexity of moving patterns of Caenorhabditis elegans and neurodegenerative disease subjects. Results obtained from analyses demonstrate that the largest recurrence eigenvalues can differentiate phenotypes of behavioral dynamics between wild type and mutant strains of Caenorhabditis elegans; and walking patterns among healthy control subjects and patients with Parkinson’s disease, Huntington’s disease, or amyotrophic lateral sclerosis.

On a topological classification of recurrence plots: Application to noise perturbed molecular dynamics time series.

In the present paper, a topological classification of recurrence plots of time series that are constructed with equal embedding dimension and delay time is proposed by defining a metric structure in the set of those recurrence plots. To achieve this, the Recurrence Plot deviation distance and the Recurrence deviation plot are introduced along with qualitative and quantitative indices, which allows for a detailed comparison of the recurrence plots of two time series and their corresponding dynamical systems. In the range of values studied, the application of additive noise on the thermostat results in a less deterministic system behavior, quite close to that of the system with the unperturbed thermostat. On the other hand, multiplicative noise of small strength results in a less deterministic system quite close to the unperturbed system behavior. For a larger strength, the system presents a behavior which is significantly different from that of the unperturbed system. The new methodology introduced here provides detailed quantitative and graphical insights for the way that noise, additive and multiplicative, influences on the morphology of recurrence plots of the unperturbed and noise perturbed time series. The results are encouraging for potential future applications on the analysis of complex dynamical systems.

Probabilistic analysis of recurrence plots generated by fractional Gaussian noise.

Recurrence plots of time series generated by discrete fractional Gaussian noise (fGn) processes are analyzed. We compute the probabilities of occurrence of consecutive recurrence points forming diagonals and verticals in the recurrence plot constructed without embedding. We focus on two recurrence quantification analysis measures related to these lines, respectively, the percent determinism and the laminarity ( ). The behavior of these two measures as a function of the fGn's Hurst exponent is investigated. We show that the dependence of the laminarity with respect to is monotonic in contrast to the percent determinism. We also show that the length of the diagonal and vertical lines involved in the computation of percent determinism and laminarity has an influence on their dependence on . Statistical tests performed on the measure support its utility to discriminate fGn processes with respect to their values. These results demonstrate that recurrence plots are suitable for the extraction of quantitative information on the correlation structure of these widespread stochastic processes.